Such a shaving apparatus is known, for example from U.S. Pat. No. 2,598,292. In this known apparatus the internal shaving member is arranged to be slidable on a shaft, which gives rise to frictional losses during use of the apparatus. The shaft is supported by resilient elements in the shaving head so that the internal shaving member and the shaft are movable, opposed by spring force, in a direction transverse to the shaft. However, as a result of this, the coupling means between the internal shaving member and the motor should also provide an adequate freedom of movement in this direction, which complicates the construction of these coupling means.